Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 50.

In this paper, we observe how the heat equation in a noncylindrical domain can arise as the asymptotic limit of a parabolic problem in a cylindrical domain, by adding a potential that vanishes outside the limit domain. This can be seen as a parabolic version of a previous work by the first and last authors, concerning the stationary case [Alvarez-Caudevilla and Lemenant, Adv. Differ. Equ. 15 (2010) 649-688]. We provide a strong convergence result for the solution by use of energetic methods and Γ-convergence technics. Then, we establish an exponential decay estimate coming from an adaptation of an argument due to B. Simon.

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DOI : 10.1051/cocv/2019023
Classification : 35A05, 35A15
Mots-clés : Parabolic problems, Gamma-convergence, energetic methods, variational methods, partial differential equations 
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     author = {\`Alvarez-Caudevilla, Pablo and Bonnivard, Matthieu and Lemenant, Antoine},
     title = {Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {26},
     year = {2020},
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     zbl = {1450.35132},
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     url = {http://www.numdam.org/articles/10.1051/cocv/2019023/}
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Àlvarez-Caudevilla, Pablo; Bonnivard, Matthieu; Lemenant, Antoine. Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 50. doi : 10.1051/cocv/2019023. http://www.numdam.org/articles/10.1051/cocv/2019023/

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